Yes, strictly speaking, Turing completeness implies a certain formal equivalence between the two programming languages. But does this does not an equivalence b

Yes, strictly speaking, Turing completeness implies a certain formal equivalence between the two programming languages. But does this does not an equivalence between systems make, for at least two reasons: 1. Different languages encourage, and make easy, different modes of thought. Lisp promots a certain view of building hte world out of recursive, replaceable pieces. 2. Different systems provide different levels of access to their internals. The vast majority of Emacs is written in Lisp, and can therefore be hooked and rewritten. Its C code is an Emacs interpreter and text editing/rendering engine. Vim provides a great deal of scripting capability and many hooks, but that's still hooks on a system rather than a system that can be freely rewritten on the fly. It feels very different, and can allow different things if Vim is missing the hook you need.